Besanko and Braeutigam, CH 12
Western University
First-Degree Price Discrimination: Making the Most from Each Consumer
Second-Degree Price Discrimination: Quantity Discounts
Third-Degree Price Discrimination: Different Prices for Different Market Segments
Tying (Tie-In Sales), Bundling
Advertising
A monopolist charges a uniform price if it sets the same price for every unit of output sold
While the monopolist captures profits due to an optimal uniform pricing policy
A firm with market power may be able to increase its profits by charging more than one price for its product through price discrimination
A policy of first-degree (or perfect) price discrimination prices each unit sold at the consumer’s maximum willingness to pay
A policy of second-degree price discrimination allows the monopolist to offer consumers a quantity discount
A policy of third-degree price discrimination offers a different price for each segment of the market (or each consumer group) when membership in a segment can be observed
Certain market features must be present for a firm to capture more surplus with price discrimination:
The demand curve is the willingness to pay curve
Since the demand curve slopes downward, the consumer buying the first unit is willing to pay a higher price than the consumer buying the second unit
If the seller can perfectly implement first-degree price discrimination, it will price each unit at the maximum amount the consumer of that unit is willing to pay
The producer sells each unit to the consumer with the highest reservation price for that unit, at that price
The monopolist will continue selling units until the reservation price exactly equals the marginal cost
The producer captures all the surplus and there is no deadweight loss
Perfect first-degree price discrimination therefore leads to an economically efficient level of output!
In the real world, it is harder to learn about willingness to pay
If you ask a customer about her willingness to pay, she will not reveal her reservation price
Suppose a monopolist has a constant marginal cost MC = 2 and faces the demand curve P = 20 − Q
Uniform pricing surplus?
First-degree price discrimination surplus?
With uniform pricing, \(MR=P+\frac{dP}{dQ}Q\)
With perfect first-degree price discrimination, only the first effect is present
When the firm sells one more unit, it does not have to reduce its price on all the other units it is already selling
So the marginal revenue curve with first-degree price discrimination is just \(MR = P\)
The marginal revenue curve equals the demand curve
A policy of second-degree price discrimination allows the monopolist to charge a different price to different consumers
While different consumers pay different prices, the reservation price of any one consumer cannot be directly observed
Sellers know that each customer’s demand curve for a good is typically downward-sloping
A seller may use this information to capture extra surplus by offering quantity discounts to consumers
Not every form of quantity discounting represents price discrimination. Often sellers offer quantity discounts because it costs them less to sell a larger quantity
One distinguishing feature of second-degree price discrimination is that the amount consumers pay for the good or service actually depends on two or more prices (parts)
For example, telecommunication services work under a multipart tariff: a subscription charge plus a usage charge
If a consumer pays one price for one block of output and another price for another block of output, the consumer faces a block tariff
Firm’s objective is to maximize profits by choosing the optimizing quantity at each block (therefore looking for the optimal block price)
The monopolist might capture additional surplus by offering a quantity discount
Charge a price for the first units (11) and a lower price (8) for any additional units
What’s the optimal block tariff?
Show mathematically on the board
Consumer’s average expenditure, average outlay, is total expenditure \(E\) divided by total quantity \(Q\)
In our previous example, \[ E = \begin{cases} \$14Q, & \text{if } Q \leq 6 \\ \$84 + \$8(Q-6), & \text{if } Q > 6 \end{cases} \]
So, the consumer’s average outlay is \[ \frac{E}{Q} = \begin{cases} \$14, & \text{if } Q \leq 6 \\ \frac{\$84 + \$8(Q-6)}{Q}, & \text{if } Q > 6 \end{cases} \]
Second Degree Price Discrimination results in a non-linear outlay schedule
Self Selection
Pareto superior allocation
\[ T=F+rQ \]
This, effectively, charges demanders of a low quantity a different average price than demanders of a high quantity
Example: include hook-up charge plus usage fee for a telephone, club membership, and so on
All customers are identical
P = 100 - Q
MC = AC = 10
What is the optimal two-part tariff?
Two steps: Draw graph on the board
Maximize the benefits to the consumers by charging r = MC = 10
Capture this benefit by setting F = consumer benefits = 4050
Any higher usage charge would result in a dead-weight loss that could not be captured by the monopolist
Any lower usage charge would result in selling at less than marginal cost
In essence, the monopolist maximizes the surplus, then sets the lump sum fee to capture the entire surplus for itself
The total surplus captured is the same as in the case of perfect price discrimination
Demand differs from one consumer to the next. High subscription and usage tariffs might capture more surplus from large-demand consumers, but small-demand consumers will not buy the service at all
The firm cannot tell apart large from small-demand consumers. Firms need to offer customers a menu of subscription and usage charges to incentivize them to self-select
If a firm can identify different consumer groups, or segments, in a market and can estimate each segment’s demand curve, the firm can practice third-degree price discrimination by setting a profit-maximizing price for each segment
Example: Movie ticket sales to senior citizens or students at a discount
How does a monopolist maximize profit with this type of price discrimination?
The optimal pricing maximizes the monopolist’s profits \[ \max_{Q_1,Q_2} P_1(Q_1)Q_1 + P_2(Q_2)Q_2- C(Q_1+Q_2) \]
\(P_i(Q_i)\) denote the inverse demand curves of group \(i\)
The optimal solution must have \[ \begin{aligned} MR_1(Q_1)&=MC(Q_1+Q_2) \\ MR_2(Q_2)&=MC(Q_1+Q_2) \end{aligned} \]
In other words, the monopolist maximizes total profits by maximizing profits from each group individually
Since marginal cost is the same in each market, \(MR_1=MR_2=MC\)
Otherwise, the monopolist could raise revenues by switching sales from the low MR group to the high MR group
Note that the price is higher in the lower elasticity demand than in the high elasticity demand
A firm that price discriminates will set a low price for the price-sensitive group and a high price for the group that is relatively price-insensitive
Senior citizens and students are more likely to be price-sensitive than the average consumer
\[ \begin{aligned} P_1\left(1-\frac{1}{ |\epsilon_{Q_1,P_1}| }\right)&=MC(Q_1+Q_2) \\ P_2\left(1-\frac{1}{ |\epsilon_{Q_2,P_2}| }\right)&=MC(Q_1+Q_2) \end{aligned} \]
if \(P_1>P_2\), then we must have
\[ \begin{aligned} 1-\frac{1}{ |\epsilon_{Q_1,P_1}| } &< 1-\frac{1}{ |\epsilon_{Q_2,P_2}| } \\ \implies |\epsilon_{Q_2,P_2}| &> |\epsilon_{Q_1,P_1}| \end{aligned} \]
The market with the higher price must have the lower price elasticity of demand.
Consumer surplus (Ex. 12.22)
Inverse elasticity pricing (LBD 12.5)
Capacity constraints (LBD 12.6)
Sorting consumers based on a consumer characteristic that
is observable by the firm (age,status) and
strongly related to a consumer unobserved characteristic that the firm would like to know (willingness to pay; elasticity of demand)
Screening Mechanisms:
Problem: High-demand consumers might buy at a price targeting low-demand consumers Ex.: Coupons easily available to everyone
How can the firm ensure that
Keep the less price-sensitive consumers from being able and/or willing to purchase the low-price version of the good
Beta consumers are better off; they prefer C rather than B. They also prefer C to A
Alpha consumers prefer A to C. Thus, they will purchase the high-price high-quality version
By reducing the quality of the low-price offer, the firm makes the low-price version unattractive for alpha consumers
A strategy of selling two (or more) versions of the product with different quality levels at different prices
Damaged goods strategy, a firm creates a low-end version of its full-priced good by deliberately damaging the product
A sales practice that allows a customer to buy one product (the tying product) only if that customer agrees to buy another product (the tied product)
Often, tying is used when customers differ by the frequency with which they wish to use a product
Tying often enables a firm to extend its market power from the tying product to the tied product
A type of tie-in sale in which a firm requires customers who buy one of its products to simultaneously buy another of its products
Bundling can increase profits when
But bundling does not always pay
| Computer | Monitor | |
|---|---|---|
| Consumer 1 | $1,200 | $600 |
| Consumer 2 | $1,500 | $400 |
| MC | $1,000 | $300 |
Without bundling: \(P_c = \$1500; P_m = \$600 ; Profit_{cm} = \$800\)
With bundling: \(P_b = \$1800; Profit_b = \$1000\)
| Computer | Monitor | |
|---|---|---|
| Consumer 1 | $1,200 | $400 |
| Consumer 2 | $1,500 | $600 |
| MC | $1,000 | $300 |
Without bundling: \(P_c = \$1500; P_m = \$600; Profit_{cm} = \$800\)
With bundling: \(P_b = \$2100; Profit_b = \$800\)
| Computer | Monitor | |
|---|---|---|
| Consumer 1 | $900 | $800 |
| Consumer 2 | $1,100 | $600 |
| Consumer 2 | $1,300 | $400 |
| Consumer 2 | $1,500 | $200 |
| MC | $1,000 | $300 |
In general, bundling a pair of goods only pays if their demands are negatively correlated
Customers who are willing to pay relatively more for good A are not willing to pay as much for good B
The reason is that the price is determined by the purchaser with the lowest reservation price
If reservation prices for the two goods are negatively correlated, bundling reduces the dispersion of reservation prices and so raises the price at which additional units can be sold
The firm can capture surplus using nonprice strategies such as advertising
By advertising, a seller hopes to increase the demand for its product, shifting the demand curve rightward and creating more surplus in the market
However, advertising is costly.
When the firm does not advertise, its maximum profit is areas I + II
When the firms spends \(A_1\) dollars on advertising, its maximum profit is areas II + III
Firms’ profit-maximization problem on advertising spending
\[ \max_{P,A} PQ(P,A)-C(Q(P,A))-A \]
with \(\frac{dQ}{dP}<0\) and \(\frac{dQ}{dA}\ge0\)
For a firm to maximize profit by advertising (expenditure on advertising A > 0) and producing a positive quantity (Q > 0), two conditions must hold:
\(MR_Q=MC_Q\), equivalently \(\frac{P-MC_Q}{P}=-\frac{1}{\epsilon_{Q,P}}\)
\(MR_A=MC_A\)
It can be shown that \[ \frac{A}{PQ}=-\frac{\epsilon_{Q,A}}{\epsilon_{Q,P}} \]
The advertising expenditure share of revenues is equal to the negative ratio of the advertising elasticity of demand to the own price elasticity of demand
Comparing two markets with the same price elasticity of demand, the advertising-to-sales ratio is higher in the market in which demand is more sensitive to advertising